Presburger sets and p-minimal fields

Details Presburger sets and p-minimal fields Presburger sets and p-minimal fields

2002-06-19

arxiv.org/abs/math/0206197v1

J. Symbolic Logic 68 (2003), 153--162

Mathematics

Logic

to appear in the Journal of Symbolic Logic

Scientific paper

We prove a cell decomposition theorem for Presburger sets and introduce a dimension theory for Z-groups with the Presburger structure. Using the cell decomposition theorem we obtain a full classification of Presburger sets up to definable bijection. We also exhibit a tight connection between the definable sets in an arbitrary p-minimal field and Presburger sets in its value group. We give a negative result about expansions of Presburger structures and prove uniform elimination of imaginaries for Presburger structures within the Presburger language.

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